Kernel Approximate Bayesian Computation for Population Genetic Inferences

Approximate Bayesian Computation (ABC), which is a likelihood-free approach for Bayesian inferences, is a rejection-based method that applies a tolerance of dissimilarity between summary statistics from observed and simulated data. Although several improvements of the algorithm have been proposed, no algorithms are free from approximation introduced by two aspects: 1) the dimensional reduction: sampling is not from the true posterior density given data but from an approximate posterior density given summary statistics; 2) the non-zero tolerance: sampling from the posterior density given summary statistics is achieved only in the limit of the zero tolerance. For the first aspect, we can improve the approximation by adding summary statistic, but the increase of the number of summary statistics could introduce additional variance caused by the low acceptance rate. Consequently, many authors have been concentrated on techniques how to choose informative summary statistics. The aim of this study is to investigate whether a new kernel-based ABC method proposed by Fukumizu et al. (2010, arXiv:1009.5736 and 2011, NIPS 24: 1549-1557) is useful for actual complex problems which demand large number of summary statistics, by applying the method to population genetic inferences. We report that, in contrast to conventional ABCs, kernel-ABC can incorporate large number of summary statistics with keeping consistency of the posterior estimates without compromising the performance of the inference.